An extention to the bayes_R2 function

[jalilian]

Hi,

This work shows that we can extend the use of the Bayesian R-square in the bayes_R2 function to a wider range of models. I've suggested some changes to the bayes_R2 function, which you can find below and in the attached file. It is not an issue, but I wanted to know whether to create an issue or submit a direct pull request.
BayesRsquared.pdf

Thank you for considering this.

Best regards,
Abdollah

bayes_R2_new <- function(fit)
{
  fam <- family(fit) # family dist. of the response
  eta <- posterior_linpred(fit) # linear predictor: eta
  mu <- fam$linkinv(eta) # conditional mean
  varfit <- apply(mu, 1, var)
  varres <- switch(fam$family, gaussian={
     as.matrix(fit, pars="sigma")^2
  }, binomial={
    v <- fam$variance(mu)
    apply(v, 1, mean)
  }, poisson={
    v <- fam$variance(mu)
    apply(v, 1, mean)
  }, Gamma={
    v <- fam$variance(mu)
    apply(v, 1, mean) / as.matrix(fit, pars="shape")
  }, beta={
    v <- fam$variance(mu)
    apply(v, 1, mean)
  }, neg_binomial_2={
    size <- as.matrix(fit, pars="reciprocal_dispersion")
    v <- fam$variance(mu, theta=c(size))
    apply(v, 1, mean)
  }, inverse.gaussian={
    v <- family(fit)$variance(mu)
    apply(v, 1, mean) / as.matrix(fit, pars="lambda")
  }, stop("the speciefied family is not implemented"))
  R2 <- varfit / (varres + varfit) # Bayesian R-squared
  attributes(R2) <- list(varfit=varfit, varres=varres)
  return(R2)
}

BayesRsquared.pdf

[jgabry]

Thanks! In the rstantools package we typically implement generic and default methods that don't take fitted model objects as input. So I think if this uses fitted model objects it would need to go into the rstanarm and/or brms bayes_R2 methods, which do take fitted model objects as input. Also tagging @avehtari.